Free vibration and static bending analysis of piezoelectric functionally graded material plates resting on one area of the two-parameter elastic foundation is firstly investigated in this paper. The third-order shear deformation theory of Reddy and 8-node plate elements are employed to derive the finite element formulations of the structures; this theory does not need any shear correction factors; however, the mechanical response of the structure is described exactly. Verification problems are performed to evaluate the accuracy of the proposed theory and mathematical model. A wide range of parameter study is investigated to figure out the effect of geometrical, physical, and material properties such as the plate dimension, volume fraction index, piezoelectric effect, elastic foundation coefficients, and the square size of the area of the foundation on the free vibration and static bending of piezoelectric functionally graded material plates. These numerical results of this work aim to contribute to scientific knowledge of these smart structures in engineering practice.

中文翻译：

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压电功能梯度材料板在两参数弹性地基上的自由振动和静态弯曲分析

本文首先研究了位于两参数弹性地基一个区域上的压电功能梯度材料板的自由振动和静态弯曲分析。利用Reddy和8节点板单元的三阶剪切变形理论推导了结构的有限元公式。该理论不需要任何剪切​​校正因子；但是，该结构的机械响应已准确描述。进行验证问题以评估所提出的理论和数学模型的准确性。进行了广泛的参数研究，以找出几何，物理和材料特性的影响，例如板尺寸，体积分数指数，压电效应，弹性地基系数，以及压电功能梯度材料板的自由振动和静态弯曲的基础面积的平方大小。这项工作的这些数值结果旨在为工程实践中的这些智能结构的科学知识做出贡献。